Econ 380 Problem Set #6 Answer Sheet. 1. (3 points) The marginal control cost curves for two air pollutant sources are given by

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1 Econ 38 Problem Set #6 Answer Sheet. (3 points) The marginal control cost curves f two air pollutant sources are given by MC = 5 + qand MC = q, where q and q denote controlled emissions by source and, respectively. With no control, each firm would emit 5 units of the pollutant. If the objective is to reduce the total (combined) pollution emissions of the two firms down to 75 units: a. What would be the cost-effective level of pollution controlled by each firm? The cost of achieving a given level of pollution control is minimized by setting the marginal cost of pollution control equal f the two firms (i.e., MC = MC). Using the above infmation, this implies that: () 5 + q = q () q = q 5 This is the first piece of infmation we need to solve the problem. The second piece of infmation we have is that we want to reduce pollution down from a total of units of emissions to only 75 units of emissions. This requires that emissions be reduced by 5 units. Mathematically, we can write this as: (3) q + q = 5 Substituting () into (3) yields: (4) ( q ) 5 + q = 5 (5) 3q = 3 (6) q =. q can be found using equation (), yielding q q = 5 = () 5 = 5. This same problem can be solved graphically as in Figure. The hizontal axis has a width of 5 (the amount of pollution emissions we want to control). At any point on this axis, q and q sum to 5. This is the graphical equivalent of equation (3). On the left-hand vertical axis we indicate MC, while the right-hand vertical axis indicates MC. Our cost-effective allocation

2 of pollution control occurs where the two marginal cost curves intersect. This is the graphical equivalent of equation (). Notice that intersection this occurs at q = 5 and q =. MC MC MC 4 3 MC 3 q q Figure b. You have been hired by the government to develop a mechanism to control this pollution, without using standards. Outline an emissions fee program. What level would the fee have to be in der to insure the government's objective? As with part a, we can solve this problem either mathematically graphically. Mathematically, we know from class that each firm will want to control pollution to the point where its marginal cost of pollution control is just equal to the tax. That is: (7) MC = T and (8) MC = T Suppose that firms did not do this. F example, suppose that firm let MC < T. It is easy to show that this is not optimal f the firm. The inequality says that the firm's marginal cost of controlling pollution is less than the tax it pays on that pollution. If the firm could control one me unit of pollution, it would save $T in taxes and spend only $MC. Since T > MC, it

3 should want to control me pollution. In fact, it will continue to control me pollution until MC = T. Combining equations (7) and (8) gives us: (9) MC = MC which in turn gives us equation () above. Any tax we institute will guarantee the "costeffectiveness" equality in equation (9). The question is, which tax level will get the firms to control exactly the amount of pollution we want controlled (i.e., q + q = 5 ). We know from problem, that the cost-effective level of pollution control f firm is q = 5. Substituting this into equation (7) yields: () T = MC = 5 + q = 5 + (5) = We can also compute the optimal tax using equation (8). Since the cost-effective amount of pollution control by firm is q =, () T = MC = q = () = Its a good idea in doing problems like this to compute T both ways as a check on your math. Graphically, the optimal tax is illustrated in Figure. MC MC MC 4 3 MC 3 T= q q Figure

4 c. The government rejects your fee program, due to the political consequences they would face from taxing business. Develop a tradable permit alternative. In particular, specify: i. How many permits should be issued. Since we want a total of 5 units of pollution controlled and want to permit 75 units of pollution, we should issue 75 permits, each allowing f unit of emissions annually. ii. How the permits are to be distributed (i.e., are they sold given away? If they are given away, to whom are they given? etc.). The method of issuing the permits is not imptant in terms of the "costeffectiveness" of the final outcome. i However, whether we sell the permits initially given them away does have an impact on the equity of the system. We may want to sell them to raise revenues. We may want to give them away in der to minimize the impact of the system on existing firms. We may want to give the permits to firms who have already put fth a lot of efft to control their pollution, rewarding them f past effts. iii. After trading, how many permits would each firm hold? As we found in class, the permit system will yield the cost-effective allocation of pollution control. Since this cresponds to q = 5 and q =, we can easily figure out the number of permits each firm should hold. Firm initially emitted 5 units of pollution, if they reduce these emissions by 5 units ( q = 5 ), then they will have 35 units of emissions left. This means they must hold 35 permits in der to comply with the law. Likewise, firm starts off with 5 units of emissions and controls units, leaving 4 units of emissions. Again, they must hold permit f each unit of emissions they have, so they must hold 4 permits. Notice that this adds up to the number of permits we issued ( = 75). iv. What price would the permits be valued at? A firm should be willing to pay its marginal cost of emissions control f a permit. This is because if they buy permit they can avoid the marginal cost of controlling that unit of pollution. Thus, at the final allocation of the permits, firm should be willing to pay: () P = MC = 5 + q = = f a permit. Likewise, firm should be willing to pay (3) P MC q ( ) = = = = ii This is true as long as there are enough firms so that one firm cannot monopolize the available permits.

5 f a permit. Notice that the firms value the permits the same. If they did not, they would want to trade permits.. True/False/Uncertain - Explain F the following statement, indicate whether it is true false uncertain. Uncertain means that it can be either true false, depending upon the circumstances. F any statement thought to be true false, state why it is true false. F any statement thought to be uncertain, identify the circumstances under which the statement would be true and false. ( point) Emission standards aimed at controlling non-unifmally mixed fund pollutants are not cost effective since they do not equalize the marginal cost of emissions control across pollution sources. This statement is, strictly speaking, false. The reason that emission standards are not cost effective in controlling non-unifmally mixed fund pollutants is that emissions standards do not equalize the marginal cost of concentration reduction. Recall that f this type of pollution, what matters is not simply the level of emissions, but the specific concentration at individual recept sites. Consider the case in which there is only one recept site of interest (e.g., a fishery) and two firms with identical costs of emissions reduction. Furtherme, suppose that firm has a transfer coefficient of. and firm two has a transfer coefficient of. (i.e., it has no impact on the concentration of the pollutant at the recept site). An emissions standard applied unifmally to the two firms would result in equal marginal costs of emissions reductions, but would still not be cost-effective. In fact, firm should not have its emissions regulated at all given that it has no impact on the recept site of interest. A cost effective policy would be to implement an ambient charge an ambient tradeable permit system.